65 citations · 118 across the 5 of their papers we have counts for
4 papers · 1 filter
An exact trace formula and zeta functions for an infinite quantum graph with a non-standard Weyl asymptotics
Sebastian Egger, Frank Steiner
We study a quantum Hamiltonian that is given by the (negative) Laplacian and an infinite chain of -like potentials with strength on the half line $\rz_{\geq0}$ and which i…
A new proof of the Voronoï summation formula
Sebastian Egger, Frank Steiner
We present a short alternative proof of the Voronoï summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics…
The Berry-Keating operator on $L^2(\rz_>,\ud x)$ and on compact quantum graphs with general self-adjoint realizations
Sebastian Endres, Frank Steiner
The Berry-Keating operator $H_{\mathrm{BK}}:= -\ui\hbar(x\frac{\ud\phantom{x}}{\ud x}+{1/2})$ [M. V. Berry and J. P. Keating, SIAM Rev. 41 (1999) 236] governing the Schrödinger dyn…
The trace formula for quantum graphs with general self adjoint boundary conditions
Jens Bolte, Sebastian Endres
We consider compact metric graphs with an arbitrary self adjoint realisation of the differential Laplacian. After discussing spectral properties of Laplacians, we prove several ver…